Phenomenological Simulation Of Spatio-temporal Patterns In Dielectric Barrier Discharge Systems

Pattern formation and self-organization are ubiquitous in nature and commonly observed in spatially extended non-equilibrium systems.During the discharge process,the space charge in the discharge air gap and the surface charge accumulated on the surface of the dielectric layer have different local dynamic behaviors,and the interaction between them gives rise to a wide variety of spatio-temporal patterns.Based on this feature,a double-layer coupled asymmetric reaction diffusion system model has been established to phenomenologically describe the pattern forming mechanism and dynamic behavior of the self-organized pattern dielectric barrier discharge systems.Two reaction-diffusion models with different dynamic behaviors are linearly coupled,Mode interaction between two different Turing modes and the pattern forming mechanisms in the non-symmetric reaction diffusion system are numerically investigated by using this two-layered coupled model.It is shown that the system gives rise to superlattice patterns if these two Turing modes satisfy the spatial resonance condition,otherwise the system yields simple patterns or superposition patterns.A suitable wave number ratio and the same symmetry are two necessary conditions for the spatial resonance of Turing modes.The eigenvalues of these two Turing modes can only vary in a certain range in order to make the two sub-system patterns have the same symmetry.Only when the long wave mode becomes the unstable mode,can it modulate the other Turing mode and result in the formation of spatiotemporal patterns with multiple scale.Moreover,it is found that the coupling strength not only determines the amplitudes of these patterns,but also affects their spatial structures.Two different types of white-eye patterns and a new super-hexagon pattern are obtained as the coupling strength increases.A new type of oscillating Turing patterns is also obtained under this linear coupled model.It is shown that the supercritical Turing modek₁ in the Lengyel-Epstein model excites and interacts with the higher-order harmonics 3^1/2k₁located in the Hopf region in the Brusselator model,and gives rise to the synchronous oscillatory hexagon pattern.As the parameter b is increased,this oscillatory hexagon pattern first undergoes period-doubling bifurcation and transits into two-period oscillation,and then into multiple-period oscillation.When the Hopf mode participates in the interaction,the pattern will eventually transit into chaos.The synchronous oscillatory hexagon pattern can only be obtained when the subcritical Turing mode k₂ in the Brusselator model is weaker than the higher-order harmonics 3^1/2k₁ located in the Hopf region and the two Turing modes do not satisfy the spatial resonance condition.The system favorites the spatial resonance and selects the super-lattice patterns when these modes are interacting each other.The interaction of Hopf mode and Turing mode can only give rise to non-synchronous oscillatory patterns.Moreover,the coupling strength also has an important effect on the oscillatory Turing patterns.Two reaction diffusion models with different dynamic behaviors are coupled nonlinearly.By setting the long wave mode as unstable mode and the short wave mode as stable mode,it is found that only the long wave mode subsystem can modulate the short wave mode subsystem,and the formed superlattice patterns can only appear in the short wave mode subsystem.When the two Turing modes are unstable,not only the long wave mode has an effect on the short wave mode,but also the short wave mode has an effect on the long wave mode.That is to say,the superlattice pattern is formed by the interaction of the two Turing modes.The simulation results show that the coupling method has an effect on the pattern formation and pattern selection under the same mode.In addition,the experimental device is built and the experimental results are consistent with the simulation results,which proves that the nonlinear coupling mode is more to describe the self-organization phenomenon in the dielectric barrier discharge system.These results are helpful for people to better understand the formation of discharge pattern in DBD systems.